W. Craig Carter

Size-Dependent Lithium Miscibility Gap in Nanoscale Li1 − x FePO4

Olivine compounds have emerged as important and enabling positive electrode materials for high-power, safe, long-life lithium rechargeable batteries. In this work, the miscibility gap in undoped Li 1-x FePO 4 is shown to contract systematically with decreasing particle size in the nanoscale regime and with increasing temperature at a constant particle size. These effects suggest that the miscibility gap completely disappears below a critical size. In the size-dependent regime, the kinetic response of nanoscale olivines should deviate from the simple size-scaling implicit in Fickian diffusion.

Microstructural Modeling and Design of Rechargeable Lithium-Ion Batteries

The properties of rechargeable lithium-ion batteries are determined by the electrochemical and kinetic properties of their constituent materials as well as by their underlying microstructure. In this paper a method is developed that uses microscopic information and constitutive material properties to calculate the response of rechargeable batteries. The method is implemented in OOF ,a public domain finite element code, so it can be applied to arbitrary two-dimensional microstructures with crystallographic anisotropy. This methodology can be used as a design tool for creating improved electrode microstructures. Several geometrical two-dimensional arrangements of particles of active material are explored to improve electrode utilization, power density, and reliability of the Li yC6uLixMn2O4 battery system. The analysis suggests battery performance could be improved by controlling the transport paths to the back of the positive porous electrode, maximizing the surface area for intercalating lithium ions, and

“Electrochemical Shock” of Intercalation Electrodes: A Fracture Mechanics Analysis

Fracture of electrode particles due to diffusion-induced stress has been implicated as a possible mechanism for capacity fade and impedance growth in lithium-ion batteries. In brittle materials, including many lithium intercalation materials, knowledge of the stress profile is necessary but insufficient to predict fracture events. We derive a fracture mechanics failure criterion for individual electrode particles and demonstrate its utility with a model system, galvanostatic charging of Li x Mn 2 O 4 . Fracture mechanics predicts a critical C-rate above which active particles fracture; this critical C-rate decreases with increasing particle size. We produce an electrochemical shock map, a graphical tool that shows regimes of failure depending on C-rate, particle size, and the materials inherent fracture toughness K Ic . Fracture dynamics are sensitive to the gradient of diffusion-induced stresses at the crack tip; as a consequence, small initial flaws grow unstably and are therefore potentially more damaging than larger initial flaws, which grow stably.

A continuum model of grain boundaries

Abstract A two-dimensional frame-invariant phase field model of grain boundaries is developed. One-dimensional analytical solutions for a stable grain boundary in a bicrystal are obtained, and equilibrium energies are computed. With an appropriate choice of functional dependencies, the grain boundary energy takes the same analytic form as the microscopic (dislocation) model of Read and Shockley [W.T. Read, W. Shockley, Phys. Rev. 78 (1950) 275]. In addition, dynamic (one-dimensional) solutions are presented, showing rotation of a small grain between two pinned grains and the shrinkage and rotation of a circular grains embedded in a larger crystal.

Extending phase field models of solidification to polycrystalline materials

Abstract We present a two-dimensional phase field model of grain boundary statics and dynamics. We begin with a brief description and physical motivation of the crystalline phase field model. The description is followed by characterization and analysis of several microstructural implications: the grain boundary energy as a function of misorientation, the liquid–grain–grain triple junction behavior, the wetting condition for a grain boundary and stabilized widths of intercalating phases at these boundaries, and evolution of a polycrystalline microstructure by solidification and impingement, followed by both grain boundary migration and grain rotation. Simulations that demonstrate these implications are presented, with a description of the numerical methods that were used to obtain them.

Simulations of microstructural evolution: anisotropic growth and coarsening

Two-dimensional calculations of anisotropic growth and coarsening are illustrated. This model is intended to simulate the development of microstructure in materials like silicon nitride. The model is comprised of an ensemble of polygonal particles with anisotropic surface energies and growth mobilities. Particle growth is modeled by linear kinetics with a driving force proportional to a difference between local supersaturation and an equilibrium chemical potential which depends on particle geometry and surface tension. The competition for solute for particle growth is calculated via the diffusion equation, and conservation laws determine the strength of sources (or sinks) in the diffusion equation. Statistics of particles size distributions are obtained and regimes of kinetic behavior are related to transitions from non-equilibrium to near-equilibrium kinetics. Computed microstructures are qualitatively comparable to those observed experimentally.

Polysulfide Flow Batteries Enabled by Percolating Nanoscale Conductor Networks

A new approach to flow battery design is demonstrated wherein diffusion-limited aggregation of nanoscale conductor particles at ∼1 vol % concentration is used to impart mixed electronic-ionic conductivity to redox solutions, forming flow electrodes with embedded current collector networks that self-heal after shear. Lithium polysulfide flow cathodes of this architecture exhibit electrochemical activity that is distributed throughout the volume of flow electrodes rather than being confined to surfaces of stationary current collectors. The nanoscale network architecture enables cycling of polysulfide solutions deep into precipitation regimes that historically have shown poor capacity utilization and reversibility and may thereby enable new flow battery designs of higher energy density and lower system cost. Lithium polysulfide half-flow cells operating in both continuous and intermittent flow mode are demonstrated for the first time.

Mechanism and Kinetics of Li2S Precipitation in Lithium-Sulfur Batteries.

The kinetics of Li2 S electrodeposition onto carbon in lithium-sulfur batteries are characterized. Electrodeposition is found to be dominated by a 2D nucleation and growth process with rate constants that depend strongly on the electrolyte solvent. Nucleation is found to require a greater overpotential than growth, which results in a morphology that is dependent on the discharge rate.

New software tools for the calculation and display of isolated and attached interfacial-energy minimizing particle shapes

Existing methods to rapidly compute interface-energy minimizing shapes with anisotropy are collected and clarified, and new methods are introduced. A description of freely available, platform-independent software for the computation and display of equilibrium geometries is provided. The software relies on a new computational method to rapidly find equilibrium geometries. It also features a graphical user interface and includes the 32 crystallographic point groups to simplify inputting interfacial energies and their associated orientations. When a particle is completely enclosed within a single interface (isolated), the software computes and provides visualization for Wulff shapes. When a particle is enclosed by two interfaces, such as a particle at a grain boundary, the software minimizes their collective interfacial energy; if one of the interfaces is planar, the computation reproduces the Winterbottom construction. When both interfaces are deformable, the software provides a new tool for calculating the particle shape and the distortions of boundaries that are attached to it, even for highly anisotropic interfaces. The properties of particles bounded by two deformable interfaces are discussed, and applications of the software are illustrated. In some cases, the software can be used as a method to infer values of relative interfacial energies from a microscopic observation.

Design criteria for electrochemical shock resistant battery electrodes

Mechanical degradation of electrode active materials (“electrochemical shock”) contributes to impedance growth of battery electrodes, but relatively few design criteria have been developed to mitigate fracture. Using micromechanical models and in situ acoustic emission experiments, we demonstrate and explain C-rate independent electrochemical shock in polycrystalline electrode materials with anisotropic Vegard coefficients. We conclude that minimizing the principal shear strain, rather than minimizing net volume change as previously suggested, is an important new design criterion for crystal chemical engineering of electrode materials for mechanical reliability. Polycrystalline particles of anisotropic Li-storage materials should be synthesized with primary crystallite sizes smaller than a material-specific critical size to avoid fracture along grain boundaries. Finally, we revise the electrochemical shock map construction to incorporate the material-specific critical microstructure feature sizes for C-rate independent electrochemical shock mechanisms, providing a simple tool for designing long-lived battery electrodes.